## ::Hasse principle

### ::concepts

In mathematics, Helmut Hasse's **local-global principle**, also known as the **Hasse principle**, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the *p*-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers *and* in the *p*-adic numbers for each prime *p*.

**Hasse principle sections**

Intro Intuition Forms representing 0 Albert\u2013Brauer\u2013Hasse\u2013Noether theorem Hasse principle for algebraic groups See also Notes References External links

PREVIOUS: Intro | NEXT: Intuition |

<< | >> |

Hasse::journal Forms::number Title::pages Solution::author Volume::theorem Rational::cubic

In mathematics, Helmut Hasse's **local-global principle**, also known as the **Hasse principle**, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the *p*-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers *and* in the *p*-adic numbers for each prime *p*.

**Hasse principle sections**

Intro Intuition Forms representing 0 Albert\u2013Brauer\u2013Hasse\u2013Noether theorem Hasse principle for algebraic groups See also Notes References External links

PREVIOUS: Intro | NEXT: Intuition |

<< | >> |